Depends on the denomination and clergy person. I can tell you as a clergy person I would not feel comfortable without having a conversation with the parents first. Baptism is a very big step with lots of responsibility. Lots of prayers (:
I just called our local church about baptism and the priest told me that both me and my husband need to be Catholic and active in the church, as well as the God parents.
I believe that he could baptize the baby and have god parents of the same religion. but I don't think you would be able to be involved firing the baptism because your not catholic and your not married. you might want to double check with his priest.